Certain workpieces, such as preformed plastic parisons to be fed to a blow-molding unit, are effectively handled in groups of, say, four parisons to be simultaneously shaped in as many mold cavities. Such a four-cavity blow molder has been described and shown in our prior U.S. Pat. No. 4,132,584, disclosing a system for the manufacture of large plastic bottles by fitting round-bottomed containers--produced by blow molding--with separately molded flat-bottomed base cups.